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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      " # Zhenfeng Liang"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# MTH9879 Homework 6\n",
      "\n",
      "Assigned: March 10, 2015.\n",
      "Due: March 24, 2015 by 6pm. \n",
      "\n",
      "Late homework **will not be accepted**.\n",
      "\n",
      "$$\n",
      "\\newcommand{\\supp}{\\mathrm{supp}}\n",
      "\\newcommand{\\E}{\\mathbb{E}}\n",
      "\\newcommand{\\Eof}[1]{\\mathbb{E}\\left[ #1 \\right]}\n",
      "\\def\\Cov{{ \\mbox{Cov} }}\n",
      "\\def\\Var{{ \\mbox{Var} }}\n",
      "\\newcommand{\\1}{\\mathbf{1} }\n",
      "\\newcommand{\\PP}{\\mathbb{P} }\n",
      "%\\newcommand{\\Pr}{\\mathrm{Pr} }\n",
      "\\newcommand{\\QQ}{\\mathbb{Q} }\n",
      "\\newcommand{\\RR}{\\mathbb{R} }\n",
      "\\newcommand{\\DD}{\\mathbb{D} }\n",
      "\\newcommand{\\HH}{\\mathbb{H} }\n",
      "\\newcommand{\\spn}{\\mathrm{span} }\n",
      "\\newcommand{\\cov}{\\mathrm{cov} }\n",
      "\\newcommand{\\sgn}{\\mathrm{sgn} }\n",
      "\\newcommand{\\HS}{\\mathcal{L}_{\\mathrm{HS}} }\n",
      "%\\newcommand{\\HS}{\\mathrm{HS} }\n",
      "\\newcommand{\\trace}{\\mathrm{trace} }\n",
      "\\newcommand{\\LL}{\\mathcal{L} }\n",
      "%\\newcommand{\\LL}{\\mathrm{L} }\n",
      "\\newcommand{\\s}{\\mathcal{S} }\n",
      "\\newcommand{\\ee}{\\mathcal{E} }\n",
      "\\newcommand{\\ff}{\\mathcal{F} }\n",
      "\\newcommand{\\hh}{\\mathcal{H} }\n",
      "\\newcommand{\\bb}{\\mathcal{B} }\n",
      "\\newcommand{\\dd}{\\mathcal{D} }\n",
      "\\newcommand{\\g}{\\mathcal{G} }\n",
      "\\newcommand{\\p}{\\partial}\n",
      "\\newcommand{\\half}{\\frac{1}{2} }\n",
      "\\newcommand{\\T}{\\mathcal{T} }\n",
      "\\newcommand{\\bi}{\\begin{itemize}}\n",
      "\\newcommand{\\ei}{\\end{itemize}}\n",
      "\\newcommand{\\beq}{\\begin{equation}}\n",
      "\\newcommand{\\eeq}{\\end{equation}}\n",
      "\\newcommand{\\beas}{\\begin{eqnarray*}}\n",
      "\\newcommand{\\eeas}{\\end{eqnarray*}}\n",
      "\\newcommand{\\cO}{\\mathcal{O}}\n",
      "\\newcommand{\\cF}{\\mathcal{F}}\n",
      "\\newcommand{\\cL}{\\mathcal{L}}\n",
      "\\newcommand{\\BS}{\\text{BS}}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color = \"red\">Homework is to be done by each student individually.  To receive full credit, you must email a completed copy of this iPython notebook to Yu Gan (yugan323@gmail.com), Fubo Shi (fubo.shi.baruch@gmail.com), and Tai-Ho Wang (tai-ho.wang@baruch.cuny.edu) by the due date and time.  All R-code must run correctly and solutions must be written up neatly in Markdown/LaTeX format.\n",
      "\n",
      "<font color=\"blue\">If you encounter problems with Markdown/LaTeX or iPython notebook, please contact your TAs Yu Gan and/or Fubo Shi.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 0. (0 points) \n",
      "Read the review article by McAleer and Medeiros and also the nice article by Barndorff-Nielsen et al."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Comparison of estimators"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Set up R environment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "download.file(url=\"http://mfe.baruch.cuny.edu/wp-content/uploads/2015/02/tq.zip\", destfile=\"tq.zip\")\n",
      "unzip(zipfile=\"tq.zip\")\n",
      "download.file(url=\"http://mfe.baruch.cuny.edu/wp-content/uploads/2015/03/RvEstimators.R.zip\", destfile=\"RvEstimators.R.zip\")\n",
      "unzip(zipfile=\"RvEstimators.R.zip\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "trying URL 'http://mfe.baruch.cuny.edu/wp-content/uploads/2015/02/tq.zip'\n",
        "Content type 'application/zip' length 695952 bytes (679 Kb)\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 679 Kb\n",
        "\n",
        "trying URL 'http://mfe.baruch.cuny.edu/wp-content/uploads/2015/03/RvEstimators.R.zip'\n",
        "Content type 'application/zip' length 2406 bytes\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 2406 bytes\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 1. (12 points) \n",
      "This assignment uses the *tqBAC* dataset from *tq.rData* and the RV estimators from *RvEstimators.R*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R \n",
      "load('tq.rData')\n",
      "library(highfrequency)\n",
      "source('RvEstimators.R')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Loading required package: xts\n",
        "Loading required package: zoo\n",
        "\n",
        "Attaching package: \u2018zoo\u2019\n",
        "\n",
        "The following objects are masked from \u2018package:base\u2019:\n",
        "\n",
        "    as.Date, as.Date.numeric\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(a) Consider the BAC trade price series.  Superimpose signature plots of the following estimators with subsampling frequency $q$ from 1 to 20: ZHOU, TSRV, MSRV, KRVTH, KRVC.  Express your results as $\\sqrt{RV}$ to make them more intuitive, as in Table 1 of Lecture 6 (recall that volatility estimates should be of the order of $2\\%$!).\n",
      "<br>\n",
      "Pay attention to good aesthetics, addling a proper legend to your plot.\n",
      "\n",
      "(b) Repeat part (a) for the BAC mid-quote series.\n",
      "\n",
      "(c) Which of these estimators do you recommend and why?  What sub-sampling frequency do you recommend based on these pictures?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# Get the price series\n",
      "px <- tqBAC$PRICE\n",
      "p <- as.numeric(px)\n",
      "log_p <- log(p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Define a function to calculate and make the \n",
      "plotEstimators <- function(log_p, m){\n",
      "    \n",
      "    # Compute the ZHOU estimator\n",
      "    rv_ZHOU <- sapply(1:m,function(q){sqrt(ZHOU(log_p, q))})\n",
      "    plot(1:m,rv_ZHOU[1:m],col=\"red\",type=\"l\",ylab=\"Square root of RV estimate\",xlab=\"Subsampling frequency q\")\n",
      "\n",
      "    # Compute the TSRV estimator\n",
      "    rv_TSRV <- sapply(1:m,function(q){sqrt(TSRV(log_p, q))})\n",
      "    lines(1:m,rv_TSRV[1:m],main=NA, col=\"blue\", type=\"l\")\n",
      "\n",
      "    # Compute the MSRV estimator\n",
      "    rv_MSRV <- sapply(1:m,function(q){sqrt(MSRV(log_p, q))})\n",
      "    lines(1:m,rv_MSRV[1:m],main=NA, col=\"purple\", type=\"l\")\n",
      "\n",
      "    # Compute the KRVTH estimator\n",
      "    rv_KRVTH <- sapply(1:m,function(q){sqrt(KRVTH(log_p, q))})\n",
      "    lines(1:m,rv_KRVTH[1:m],main=NA, col=\"yellow\", type=\"l\")\n",
      "\n",
      "    # Compute the KRVC estimator\n",
      "    rv_KRVC <- sapply(1:m,function(q){sqrt(KRVC(log_p, q))})\n",
      "    lines(1:m,rv_KRVC[1:m],main=NA, col=\"green\", type=\"l\")\n",
      "\n",
      "    legend(\"topright\", c(\"ZHOU\",\"TSRV\",\"MSRV\",\"KRVTH\",\"KRVC\"),\n",
      "           lty = c(1,1,1,1,1), col=c(\"red\",\"blue\",\"yellow\",\"purple\",\"green\"))\n",
      "}\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# The maximum subsampling frequency you would like to plot\n",
      "m <- 20\n",
      "\n",
      "# Part (a)\n",
      "# Passing the log price series\n",
      "plotEstimators(log_p,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Y30AjyjuqAtPsAJiZ2WToCUqZVNk3Nb/z2ebM6Od0GFpBysogcKqPmxsdhqYqfPnll4GB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\nEjQhhPDU/wPXJMxMHTmeYwAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part(b)\n",
      "\n",
      "bid <- as.numeric(tqBAC$BID)\n",
      "offer <- as.numeric(tqBAC$OFR)\n",
      "mid <- (bid + offer)/2\n",
      "log_mid <- log(mid)\n",
      "\n",
      "# Passing the log mid quote as the price series\n",
      "plotEstimators(log_mid,m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GAMhEpgc8DuOwPvTrd1lVqPZH//7o/xt+C0CAHezGYdz3+J4jy/+/FBZi1CiMHfslVPjb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\nJLaXT9Sz5gAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###(c)\n",
      "\n",
      "I would recommend MSRV estimator. We can see in both mid quote and trade price pictures, MSRV is the smoothest curve around 2% which is a empirical reasonable number. \n",
      "\n",
      "In both pictures, we could see MSRV is stable after q = 15, so, I would choose q = 15."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Epps effect"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 2. (14 points) \n",
      "For this assignment, use the *tqBAC* and  *tqC* datasets from *tq.rData*, the function *getSymbols* from the *quantmod* package, and the function *aggregatets* from the * highfrequency* package."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "load('tq.rData')\n",
      "library(highfrequency)\n",
      "library(quantmod)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Loading required package: TTR\n",
        "Version 0.4-0 included new data defaults. See ?getSymbols.\n",
        "\n",
        "Attaching package: \u2018quantmod\u2019\n",
        "\n",
        "The following objects are masked from \u2018package:highfrequency\u2019:\n",
        "\n",
        "    getPrice, has.Qty\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "(a) Write a function to aggregate a *tq* object (such as *tqBAC*) to the nearest $k$ seconds. <br>\n",
      "(Hint: Use the function *aggregatets(.)*).\n",
      "\n",
      "(b) Write a function to compute the correlation between two high-frequency log return series (in *tq* format) where the underlying prices have been aggregated to the nearest $k$ seconds.\n",
      "\n",
      "(c) Plot the correlation between BAC and C returns where these returns are sampled every $k$ seconds, with $ k  \\in \\{2,3,4,. .., 599,600\\} $.  Use a kernel smoothing function such as *ksmooth* to smooth your results.  Make sure the aesthetics are good with nice labels etc.\n",
      "\n",
      "(d)  Is your plot consistent with the Epps effect?  What was the intraday correlation between BAC and C returns on 04-May-2012?\n",
      "\n",
      "(e) Use the function *getSymbols* from *quantmod* to download daily data for BAC and C from 01-Jan-2012 to 31-Dec-2012.  What was the historical correlation of daily BAC and C returns over that period?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (a)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (a)\n",
      "# Funtion to aggregate a tq object (such as tqBAC) to the nearest numberOfPerionds timescale. \n",
      "aggregateTQ <- function(tqObj, numberOfPeriods, timescale){\n",
      "    agg = aggregatets(tqObj, k = numberOfPeriods, on = timescale)\n",
      "    return (agg)\n",
      "}\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (b)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (b)\n",
      "# Function to compute the correlation between two high-frequency log return series (in tq format) \n",
      "# where the underlying prices have been aggregated to the nearest k seconds.\n",
      "\n",
      "Cal_Corr <- function(logReturnSeries1, logReturnSeries2){\n",
      "    return (cor(logReturnSeries1, logReturnSeries2))\n",
      "}\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (c)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# Part (c)\n",
      "CalAggregatedCorr_k_seconds_frequency <- function(tqObj1, tqObj2, k){\n",
      "    \n",
      "    aggObj1 <- aggregateTQ(tqObj1, k, \"secs\")\n",
      "    aggObj2 <- aggregateTQ(tqObj2, k, \"secs\")\n",
      "    \n",
      "    p1 <- as.numeric(aggObj1$PRICE)\n",
      "    p2 <- as.numeric(aggObj2$PRICE)\n",
      "    \n",
      "    r1 <- diff(log(p1))\n",
      "    r2 <- diff(log(p2))\n",
      "    \n",
      "    return (Cal_Corr(r1, r2))\n",
      "} \n",
      "\n",
      "CorrWrapper <- function(k){\n",
      "    return (CalAggregatedCorr_k_seconds_frequency(tqBAC, tqC, k))\n",
      "}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "nn <- 600\n",
      "\n",
      "# compute the correlation curve\n",
      "CorrVec <- sapply(2:nn, CorrWrapper)\n",
      "\n",
      "# Smooth the curve\n",
      "SmoothedOne <- ksmooth(2:nn, CorrVec, bandwidth = 10)$y\n",
      "\n",
      "plot(2:nn,CorrVec,col=\"red\",type=\"l\",ylab=\"Correlation\",xlab=\"Sampling interval k\", \n",
      "     main = \"Correlation between the price from tqBAC and tqC\")\n",
      "lines(2:nn,SmoothedOne,main=NA, col=\"blue\", type=\"l\")\n",
      "\n",
      "legend(\"topright\", c(\"Original\",\"Smoothed\"), lty = c(1,1), col=c(\"red\",\"blue\"))\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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BphEHhZJydKObXay5O0rptoMmvlVdjrqbHcIy7fUiN7fLGbTDIZejG3FwnE4G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Ny4gRW06WIIyCEOmv9osMhicQzTgx7mJCF5s7wcl1566EVxXHrppVOmTOno6PB6vVVVVV/72teu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\nYBQKGgCAUf8POLAJcK9fFVYAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (d)\n",
      "\n",
      "My result is consistent with Epps effect. From the above picture, we could see when the sampling interval k decrease, which means sampling frequency increases, the correlation tends to zero."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "IntradayCorrelation <- CorrWrapper(2)\n",
      "cat(\"The intraday correlation between BAC and C returns on 04-May-2012 is\", IntradayCorrelation)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "The intraday correlation between BAC and C returns on 04-May-2012 is 0.04299153"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (e)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "\n",
      "getSymbols(\"BAC\", from = as.Date(\"2012-01-01\"), to = as.Date(\"2012-12-31\"))\n",
      "getSymbols(\"C\", from = as.Date(\"2012-01-01\"), to = as.Date(\"2012-12-31\"))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "    As of 0.4-0, \u2018getSymbols\u2019 uses env=parent.frame() and\n",
        " auto.assign=TRUE by default.\n",
        "\n",
        " This  behavior  will be  phased out in 0.5-0  when the call  will\n",
        " default to use auto.assign=FALSE. getOption(\"getSymbols.env\") and \n",
        " getOptions(\"getSymbols.auto.assign\") are now checked for alternate defaults\n",
        "\n",
        " This message is shown once per session and may be disabled by setting \n",
        " options(\"getSymbols.warning4.0\"=FALSE). See ?getSymbols for more details.\n",
        "[1] \"C\"\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# We use the adjusted price\n",
      "adjusted_P_BAC <- as.numeric(BAC$BAC.Adjusted)\n",
      "adjusted_P_C <- as.numeric(C$C.Adjusted)\n",
      "correlation <- cor(diff(log(adjusted_P_BAC)), diff(log(adjusted_P_C)))\n",
      "cat(\"The historical correlation of daily BAC and C returns over that period is\", correlation)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "The historical correlation of daily BAC and C returns over that period is 0.7996545"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Hayashi-Yoshida estimator"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 3. (2 points) \n",
      "Show that when two time series $p^{(1)}$ and $p^{(2)}$ are synchronous, the Hayashi-Yoshida estimator coincides with the realized covariance estimator."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 3\n",
      "\n",
      "The Hayashi-Yoshida estimator\n",
      "\n",
      "$$HY_t=\\sum_{i \\leq t}\\,\\sum_{j \\leq t}\\,(p^{(1)}_i-p^{(1)}_{i-1})\\,(p^{(2)}_j-p^{(2)}_{j-1})\\,v_{ij}$$\n",
      "where\n",
      "\n",
      "$$v_{ij}={\\bf 1}_{[t_{i-1},t_i] \\cap [t_{j-1},t_j] \\neq \\emptyset}$$\n",
      "\n",
      "When they are synchronous, $v_{ij} = 1$, $HY_t=\\sum_{i \\leq t}\\,\\sum_{j \\leq t}\\,(\\Delta p^{(1)}_i)\\,(\\Delta p^{(2)}_j)$, we divide it by $T$, and would have the relized covariance."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Fulvio Corsi's HAR-RV model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following code loads the data of SPX realized volatility required for this problem. Data were downloaded from the Oxford-Man website"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "download.file(url=\"http://mfe.baruch.cuny.edu/wp-content/uploads/2015/03/spx_krv.rData_.zip\", destfile=\"spx_krv.zip\")\n",
      "unzip(zipfile=\"spx_krv.zip\")\n",
      "load(\"spx_krv.rData\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "trying URL 'http://mfe.baruch.cuny.edu/wp-content/uploads/2015/03/spx_krv.rData_.zip'\n",
        "Content type 'application/zip' length 39431 bytes (38 Kb)\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 38 Kb\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%R data.frame(head(spx.krv))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([[ 0.00016073,  0.0002644 ,  0.00030465,  0.00014858,  0.00012327,\n",
        "         0.00013069]])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 4. (12 points)\n",
      "\n",
      "(a) Rerun the HAR-RV example code using the 2008 *DJI_RV* sample from the *highfrequency* package.\n",
      "\n",
      "(b) Repeat the analysis of part (a) with *spx.krv* restricted to 2008.\n",
      "\n",
      "(c) Tabulate the HAR-RV coefficients for the two 2008 datasets.  Are they similar or do they differ?  Is most weight on the 1-day, 5-day, or 22-day RV?\n",
      "\n",
      "(d) Using *quantmod* download daily VIX data.  Subset this data to 2008 and plot ${\\rm VIX}^2$.\n",
      "\n",
      "(e)  Plot SPX RV and superimpose DJI RV for 2008. Superimpose a plot of $\\text{VIX}^2$, adding a scale on the right hand axis (see how this is done in the lecture iPython notebook). Comment on the resulting plot.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (a)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R \n",
      "\n",
      "# Forecasting daily Realized volatility for DJI 2008 using the basic harModel: HARRV\n",
      "\n",
      "data(realized_library); #Get sample daily Realized Volatility data\n",
      "DJI_RV <- realized_library$Dow.Jones.Industrials.Realized.Variance; #Select DJI\n",
      "DJI_RV <- DJI_RV[!is.na(DJI_RV)] #Remove NA's\n",
      "DJI_RV <- DJI_RV['2008']\n",
      "\n",
      "x <- harModel(data=DJI_RV , periods = c(1,5,22), RVest = c(\"rCov\"), type=\"HARRV\",h=1,transform=NULL)\n",
      "plot(x)\n",
      "print(summary(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "Call:\n",
        "\"RV1 = beta0  +  beta1 * RV1 +  beta2 * RV5 +  beta3 * RV22\"\n",
        "\n",
        "Residuals:\n",
        "       Min         1Q     Median         3Q        Max \n",
        "-0.0017683 -0.0000626 -0.0000427 -0.0000087  0.0044331 \n",
        "\n",
        "Coefficients:\n",
        "       Estimate Std. Error t value Pr(>|t|)    \n",
        "beta0 4.432e-05  3.695e-05   1.200   0.2315    \n",
        "beta1 1.586e-01  8.089e-02   1.960   0.0512 .  \n",
        "beta2 6.213e-01  1.362e-01   4.560 8.36e-06 ***\n",
        "beta3 8.721e-02  1.217e-01   0.716   0.4745    \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "\n",
        "Residual standard error: 0.0004344 on 227 degrees of freedom\n",
        "Multiple R-squared:  0.4679,\tAdjusted R-squared:  0.4608 \n",
        "F-statistic: 66.53 on 3 and 227 DF,  p-value: < 2.2e-16\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NwN3d/ccffxw6dCgPRyeENIxaHILEXw/a1dU1NDS0U6dOJpNp0KBBvB2XENIw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\nMH8+10MiEuHECTg7IzCwyvAQTdMYCbqkpOT7779v3769rq6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u7u7z589v0aKF\nh4dHREREr169RCLRvHnzuLeHh4e7uroaGBh4e3unpqaqdVeYtx1L0Mxb5/r16927d4+NjS0tLfXz\n8zt06NDZs2fXr1+flZWVk5Pj7+//7bffpqSktGvXLjAwUN3BMm81LXUHwDCNzdLScvLkyQCGDh2a\nn59v+8Lz58+vXbvm6ek5atQoAKtXrzYzM1MoFAKBQN0hM28plqCZt46hoSH3QEtLy8LCovwxgOTk\n5DNnztjZ2XGFQqEwMzPT0tJSHWEyDEvQDFOJpaWll5fX4cOHASgUisjIyPIMzjCNj/VBM0wFHx+f\n8PDwEydOZGdnL1y4cN68eTweT91BMW8vlqAZpoKFhcWePXu+/PJLW1vbW7du7dq1S90RMW81Ng6a\nYRhGQ7EWNMMwjIZiCZphGEZDsQTNMAyjoViCZhiG0VAsQTMMw2golqAZhmE0FEvQDMMwGoolaIZh\nGA3FEjTDMIyGYgmaYRhGQ7EEzTAMo6FYgmYYhtFQLEEzDMNoKJagGYZhNBRL0AzDMBqKJWiGYRgN\nxRI0wzCMhmIJmmEYRkP9f71HRGc4rKgqAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (b)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "# part(b)\n",
      "\n",
      "# Forecasting daily Realized volatility for SPX 2008 using the basic harModel: HARRV\n",
      "SPX_KRV <- spx.krv;\n",
      "SPX_KRV <- SPX_KRV[!is.na(SPX_KRV)] #Remove NA's\n",
      "SPX_KRV <- SPX_KRV['2008']\n",
      "\n",
      "x_krv <- harModel(data=SPX_KRV , periods = c(1,5,22), RVest = c(\"rCov\"), type=\"HARRV\",h=1,transform=NULL)\n",
      "plot(x_krv)\n",
      "print(summary(x_krv))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "\n",
        "Call:\n",
        "\"RV1 = beta0  +  beta1 * RV1 +  beta2 * RV5 +  beta3 * RV22\"\n",
        "\n",
        "Residuals:\n",
        "       Min         1Q     Median         3Q        Max \n",
        "-0.0022396 -0.0001219 -0.0000725 -0.0000176  0.0079141 \n",
        "\n",
        "Coefficients:\n",
        "       Estimate Std. Error t value Pr(>|t|)    \n",
        "beta0 7.164e-05  5.960e-05   1.202  0.23067    \n",
        "beta1 1.523e-01  8.218e-02   1.853  0.06526 .  \n",
        "beta2 5.512e-01  1.415e-01   3.896  0.00013 ***\n",
        "beta3 1.501e-01  1.324e-01   1.134  0.25801    \n",
        "---\n",
        "Signif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n",
        "\n",
        "Residual standard error: 0.0006787 on 220 degrees of freedom\n",
        "Multiple R-squared:  0.4096,\tAdjusted R-squared:  0.4015 \n",
        "F-statistic: 50.87 on 3 and 220 DF,  p-value: < 2.2e-16\n",
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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eeeUVMzOaf00In1BA85IpgrK6unr58uVBQUESicTOzs7CwiIwMHDJkiV1dXUm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\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (c)\n",
      "\n",
      "|Coefficients   | DJi RV | SPX KRV |\n",
      "|---|--------|--------|\n",
      "| $\\beta_0$  | 4.432e-05  |   7.164e-05 |\n",
      "| $\\beta_D$ | 1.586e-01   |   1.523e-01 |\n",
      "| $\\beta_W$  | 6.213e-01  |   5.512e-01 |\n",
      "| $\\beta_M$  | 8.721e-02  |   1.501e-01 |\n",
      "\n",
      "We can see above, they are very similar.\n",
      "For DJI, 1-day RV is the most important. For SPX, 1-day RV is almost the most most important. So, we can say that 1-day RV is the most important."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (d)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "getSymbols(c(\"^VIX\"), from = as.Date(\"2008-01-01\"), to = as.Date(\"2008-12-31\"))\n",
      "plot(VIX$VIX.Adjusted,main = \"2008, VIX\", ylab=\"Daily adjusted price\",xlab=\"Time\", major.ticks= \"months\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "    As of 0.4-0, \u2018getSymbols\u2019 uses env=parent.frame() and\n",
        " auto.assign=TRUE by default.\n",
        "\n",
        " This  behavior  will be  phased out in 0.5-0  when the call  will\n",
        " default to use auto.assign=FALSE. getOption(\"getSymbols.env\") and \n",
        " getOptions(\"getSymbols.auto.assign\") are now checked for alternate defaults\n",
        "\n",
        " This message is shown once per session and may be disabled by setting \n",
        " options(\"getSymbols.warning4.0\"=FALSE). See ?getSymbols for more details.\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QYPaVbYSz6xVU/gTwX92g0kR3xYNJVnUgJhWDuknO3SReFz8ieBivVfnfTWad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\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## (e)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "par(mar = c(5,5,2,5),cex=0.8)\n",
      "plot(DJI_RV,main = \"Realized volatility in 2008\", ylab=\"Daily realized variance\",xlab=\"Time\", major.ticks= \"months\")\n",
      "lines(DJI_RV, col = \"red\")\n",
      "lines(SPX_KRV, col = \"blue\")\n",
      "par(new = T)\n",
      "plot(VIX$VIX.Adjusted, col = \"yellow\", axes = F, xlab = NA, ylab = NA,main=NA)\n",
      "axis(side = 4)\n",
      "mtext(side = 4, line = 3, \"VIX Adjusted\")\n",
      "\n",
      "legend(\"topleft\", c(\"DJI RV\",\"SPX RV\",\"VIX Adjusted\"), lty = c(1,1,1), col=c(\"red\",\"blue\",\"yellow\"))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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gY8MKMsZ8MeVBD9xRJca+FYolhaWsrIy88lx5eXmEImKJS7wDdGVl5bXXXjt9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\n3dsXLdFXcH7X+LGX9jAyHUZj8+bNo6+4AkD5Aw94Pv4YgJ0oP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      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Comment:\n",
      "\n",
      "They are clearly positive correlated."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}